Über die Verallgemeinerung eines gewissen Iterationsverfahrens für die Lösung spezieller linearer algebraischer Gleichungssysteme. (On a generalization of a certain iterative method for the solution of special systems of linear algebraic equations). (German) Zbl 0698.65022

The author continues his study of iterative methods for the solution of linear systems \(Ax=b\) where the methods contain a number of parameters to speed up convergence [ibid. 31, 420-426 (1986; Zbl 0615.65037) and 34, 265-273 (1989; Zbl 0685.65019)].
He now considers the case where the matrix may be reduced to block upper triangular form by permutations. The iteration matrix is then also simpler, and by a suitable choice of the parameters its spectral radius may be made smaller than 1.
The paper does not contain numerical examples to show how the iteration matrix can be computed.
Reviewer: W.Govaerts


65F10 Iterative numerical methods for linear systems
Full Text: EuDML


[1] D. M. Young: Iterative solution of large systems. Academic Press, 1971, New York and London.
[2] M. Šisler: Über ein mehrparametnges Iterationsverfahren für lineare Gleichungssysteme mit einer dünnen Matrix. Apl. mat. 31 (1986), 420-426. · Zbl 0615.65037
[3] M. Šisler: Beitrag zu rnehrparametrigen Iterationsverfahren für spezielle lineare Gleichungssysteme. Apl. mat. 34 (1989), 265-273. · Zbl 0685.65019
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